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CHEM 342. Spring 2002. Problem Set #8. Mortimer Chapters 19, 20. Note: Please note that B h 8 2 cI where B is expressed in cm1; and B h 8 2 I where B is expressed in Hz. Rotating Diatomic Molecules 1. For a diatomic molecule in a 1 electronic state, we observe a microwave transition from J = 1 to J = 2 in the presence of an electric field. How many lines will appear in the spectrum? 2. Which of the following diatomic molecules have a rotational microwave spectrum: IF, O 2 , KCl, Cl 2 . 3. Calculate the bond length of 1.14 10 26 kg . 12 C 16O using B 1.9302 cm 1 and the reduced mass is Vibrating Diatomic Molecules 4. Which of the following vibrational transitions will be observed for a diatomic molecule (treated as a harmonic oscillator): v = 1 to v = 3; v = 2 to v = 3; v = 5 to v = 4. 5. Calculate the frequency of the J = 3 to J = 4 transition in the pure rotational absorption spectrum of 14 N 16O . The equilibrium bond length is 115 pm. Assume no centrifugal distortion. The mass of a nitrogen atom is 14.003 amu; the mass of an oxygen atom is 15.995 amu; and the conversion factor is 1.6605 10 27 kg/amu . Rotation of Polyatomic Molecules 6. Identify the molecules that will exhibit a pure rotational absorption microwave spectrum: N 2 O, NO2 , CClF3 , NF3 , SF6 , CH 4 , CO2 . 7. What information about the molecular geometry for N 2 O can be determined from knowing that a pure rotational absorption spectrum is observed for this molecule? 8. The moment of inertia about an axis perpendicular to the principal axis ( I ) for NH 3 is 2.82 10 47 kg m 2 . There are different types of rigid rotors: linear, spherical top, prolate symmetric top, oblate symmetric top, asymmetric top. Which type of rotor is NH 3 ? Calculate the separation (expressed in cm 1 ) of the pure rotational spectrum lines for NH 3 . Hint: The moment of inertia about the principal axis is given by I ll 2m H R 2 1 cos , where the mass of a hydrogen atom = mH = 1.6735 10 27 kg ; the N-H bond length = R = 1.014 10 10 m ; and the bond angle is 106.78. The moment of inertia about the principal axis is I ll . 9. The molecule CClF3 is a prolate symmetrical top with A 0.1908 cm 1 and B 0.1111 cm 1 . Calculate the energy corresponding to J = 2 and K = 1. Vibration of Polyatomic Molecules 10. Consider the vibrational mode that corresponds to the uniform expansion of the benzene ring. Is it infrared active? CHEM 342. Spring 2002. Problem Set #8. Mortimer Chapters 19, 20. Raman Spectroscopy 11. Explain the difference between Stokes and anti-Stokes lines in Raman Spectroscopy. PLEASE NOTE The work you hand in should be neat and well organized, and it should show the strategy and steps you used in solving the problems, as well as the bottom-line answers (or solutions). In grading the problems, both your work-up and your final answers/solutions will be examined and evaluated. The work handed in for grading must carry a pledge that the work is entirely yours and was done without any collaboration with other persons (except for the course instructor and TA's). You are encouraged to work with others in doing the exercises and problems found in the textbook, but all work handed in for grading should be done independently.